Vector Question no. 1 For any vector a and b , ( a ✕ b ) 2 looks_one a 2 - b 2 looks_two a 2 + b 2 looks_3 a 2 b 2 -( a.b ) 2 looks_4 none of these Answer Option looks_3 a 2 b 2 -( a.b ) 2 Solution Solution : ( a ✕ b ) = | a || b |sinθ n ( a ✕ b ) 2 = | a | 2 | b | 2 sin 2 θ = | a | 2 | b | 2 ( 1 - cos 2 θ) = | a | 2 | b | 2 - | a | 2 | b | 2 cos 2 θ = | a | 2 | b | 2 -( a.b ) 2 Question no. 2 A unit vector prependicular to 3 i + 2 j - k and 12 i + 5 j -5 k , is looks_one (5 i - 3 j -9 k )/√ 115 looks_two (5 i + 3 j -9 k )/√ 115 looks_3 (-5 i + 3 j -9 k )/√ 115 looks_4 (5 i + 3 j +9 k )/√ 115 Answer option looks_3 (-5 i + 3 j -9 k )/√ 115 solution Solution : Question no. 3 For any vector a and b ,if a ✕ b =0 , then looks_one a=0 looks_two b=0 looks_3 not parallel looks_4 n...

Quadratic equation Question no. 1 If the sum of the roots of the quadratic equation ax 2 + bx + c = 0 is equal to the sum of the squares of their reciprocals, then are in (2003) looks_one Arithmetic progression looks_two Geometric progression looks_3 Harmonic progression looks_4 Arithmetic−Geometric−progression Answer Option 1. 0 Solution very soon 16 Question no. 2 The number of real solutions of the equation x 2 − 3 |x| + 2 = 0 is (2003) looks_one 2 looks_two 4 looks_3 3 looks_4 1 Answer option Solution ver soon 2 Question no. 3 The value of ‘a’ for which one root of the quadratic equation (a 2 − 5a + 3) x 2 + (3a − 1) x + 2 = 0 is twice as large as the other, is (2003) looks_one 2/3 looks_two -2/3 looks_3 1/3 looks_4 -1/3 Answer option Solution very soon 3 Question no. 4 Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the root...

quadratic equations Question no. 16 If P(x)= ax 2 +bx+c=0 and Q(x)= -ax 2 +bx+c=0, where ac≠0 then P(x).Q(x)=0 has at least looks_one four real roots looks_two two real roots looks_3 four imaginary roots looks_4 none of these Answer Option looks_two two real roots Solution ax 2 +bx+c=0 has D = b 2 -4ac , D can be less than 0 or greater than 0 , there is a possibility of having complex roots or real roots. -ax 2 +bx+c=0 has D = b 2 + 4ac , D is always greater than or equal to 0 , so it has 2 reals roots , So P(x)Q(x) = 0 has atleast 2 real roots Question no. 17 If the roots of the given equation 2x 2 +3(λ-2)x+ λ+4=0 be equal in magnitude but opposite in sign, then λ = looks_one 1 looks_two 2 looks_3 3 looks_4 2/3 Answer option looks_two 2 solution let A and B are two roots of given quadratic equation A + B = 0 3 (λ -2)/ 2 = 0 λ = 2 Question no. 18 If a+b+c=0, then the roots of ...

quadratic equations Question no. 1 Let one root of ax 2 +bx+c=0 , where a ,b ,c are integers, be 3+ √ 5 ,then the other root is looks_one 3-√ 5 looks_two 3 looks_3 √ 5 looks_4 none of these Answer Option looks_one 3-√ 5 Solution Whenever roots are in complex or in square roots form , then they are conjugate to each other therefore , the other root is 3-√ 5 Question no. 2 The roots of the given equation (p-q)x 2 +(q-r)x+(r-p)=0 looks_one (p-q)/(r-p),1 looks_two (q-r)/(p-q),1 looks_3 (r-p)/(p-q),1 looks_4 (q-r)/(q-p),1 Answer looks_3 (r-p)/(p-q),1 solution (p-q)x 2 +(q-r)x+(r-p)=0 Question no. 3 If one root of equations x 2 +px+12=0 is 4 ,while the root of equations x 2 +px+q=0 are equal, then the value of q is looks_one 4 looks_two 4/49 looks_3 49/4 looks_4 none of these answer Option looks_3 49/4 solution x 2 +px+12=0 (4) 2 + 4p + 12 = 0 p = -7 Roots...